Finite Group Databasebeta

← C2×#20256034 #27095847

Subgroups — C2×#20256034 #27095847

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689842C211yesmaximal, characteristic, complemented
2C2×#15689829C211yesmaximal, characteristic, complemented
3#20256034C2116yesmaximal, direct product factor
4C2×#15689476C211yesmaximal, characteristic, complemented
5C2×#15689472C211yesmaximal, characteristic, complemented
6C2×#15689428C211yesmaximal, characteristic, complemented
7C2×#15689427C211yesmaximal, characteristic, complemented
8C2×#15689411C211yesmaximal, characteristic, complemented
9C2×#15689337C211yesmaximal, characteristic
10C2×#15689335C211yesmaximal, characteristic
11C2×#15689327C211yesmaximal, characteristic, complemented
12C2×C8×Dic94C211yesmaximal, characteristic, complemented
13C2×C4×#10625325C211yesmaximal, characteristic, complemented
14C2×#15689208C211yesmaximal, characteristic, complemented
15C2×#15689203C211yesmaximal, characteristic
16C2×C47×#488C211yesmaximal, characteristic, complemented
17C22×#10625325C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19C22×#10625334C2211yescharacteristic
20#15689842—24no—
21#15689842C2218yescomplemented
22#15689829—24no—
23#15689829C2218yescomplemented
24C2×#13094023C2211yescharacteristic
25C2×#13094022C2211yescharacteristic
26C2×#13094017—21no—
27C2×#13094017—21no—
28C2×#13094015C2211yescharacteristic
29C2×#13094011C2211yescharacteristic
30C2×#13094004—21no—
31C2×#13094002—21no—
32C2×#13094002—21no—
33C2×#13094001—21no—
34C2×Q8×Dic47C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×Dic94C2211yescharacteristic
37C2×C4×D188C2211yescharacteristic
38C2×D4×Dic47C2211yescharacteristic
39C2×#13093986C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×#13093980—21no—
42C2×C4⋊C4×D47—21no—
43#15689476C2218yescomplemented
44#15689472C2218yescomplemented
45#15689428C2218yescomplemented
46#15689427C2218yescomplemented
47#15689411C2218yescomplemented
48#15689337C2218yes—
49#15689335C2218yes—
50#15689327C2218yescomplemented
51C8×Dic94C2218yescomplemented
52C4×#10625325C2218yescomplemented
53#15689208C2218yescomplemented
54#15689203C2218yes—
55C2×#13093957C2211yescharacteristic
56C2×#13093956C2211yescharacteristic
57C2×#13093955C2211yescharacteristic
58C2×C4⋊(C47⋊C8)C2211yescharacteristic
59C2×Dic47⋊C8C2211yescharacteristic
60C2×Dic47⋊C8C2211yescharacteristic
61C2×#13093949C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093947C2211yescharacteristic
64C2×#13093947C2211yescharacteristic
65C2×#13093946C2211yescharacteristic
66C2×#13093945C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C2×#125×C47C2211yescharacteristic
70C2×#124×C47C2211yescharacteristic
71C47×#488C2218yescomplemented
72C2×#103×C47C2211yescharacteristic
73C2×#103×C47C2211yescharacteristic
74C2×#102×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94D411yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C23×Dic47—21no—
82C22×C4×D47—21no—
83C22×C4×D47—21no—
84C22×C4×D47—21no—
85C2×#10625325—24no—
86C2×#10625325C2314yes—
87C2×#10625336—24no—
88C2×#10625336C2314yes—
89C2×#10625334—24no—
90C2×#10625334C2314yes—
91C22×C47⋊C8C2311yescharacteristic
92C22×C47⋊C8C2311yescharacteristic
93#13094023—22no—
94#13094023C2314yes—
95#13094022—22no—
96#13094022C2314yes—
97#13094017—28no—
98#13094017—28no—
99#13094015—22no—
100#13094015C2314yes—
101#13094011—22no—
102#13094011C2314yes—
103#13094004—28no—
104#13094002—28no—
105#13094002—28no—
106#13094001—28no—
107Q8×Dic47—22no—
108Q8×Dic47C2314yes—
109C4×Dic94—22no—
110C4×Dic94D414yes—
111C4×Dic94C2314yes—
112C4×Dic94C2314yes—
113C4×D188—22no—
114C4×D188C2314yes—
115D4×Dic47—22no—
116D4×Dic47C2314yes—
117#13093986—22no—
118#13093986—22no—
119#13093986C2314yes—
120#13093986C2314yes—
121#13093980—28no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47—21no—
124C2×C4⋊Dic47D411yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×C4⋊Dic47C2311yescharacteristic
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4—21no—
132C2×Dic47⋊C4D411yescharacteristic
133C2×Dic47⋊C4D411yescharacteristic
134C4⋊C4×D47—28no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×(C2×D47)⋊C4—21no—
139C2×(C2×D47)⋊C4—21no—
140C2×(C2×D47)⋊C4—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143C2×C4×Dic47C2311yescharacteristic
144C2×C4×Dic47C2311yescharacteristic
145#13093957C2314yes—
146#13093956C2314yes—
147#13093955C2314yes—
148C4⋊(C47⋊C8)C2314yes—
149Dic47⋊C8C2314yes—
150Dic47⋊C8C2314yes—
151#13093949C2314yes—
152#13093948C2314yes—
153#13093947C2314yes—
154#13093947C2314yes—
155#13093946C2314yes—
156#13093945C2314yes—
157C8×Dic47C2314yes—
158C8×Dic47C2314yes—
159C22×Q8×C47C2311yescharacteristic
160C22×D4×C47C2311yescharacteristic
161C22×C8×C47C2311yescharacteristic
162C22×C8×C47C2311yescharacteristic
163#125×C47—22no—
164#125×C47C2314yes—
165#124×C47—22no—
166#124×C47C2314yes—
167C2×C4⋊C4×C47—21no—
168C2×C4⋊C4×C47—21no—
169C2×C4⋊C4×C47C2311yescharacteristic
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C22⋊C4×C47—21no—
172C2×C22⋊C4×C47—21no—
173C2×C42×C47C2311yescharacteristic
174#103×C47C2314yes—
175#103×C47C2314yes—
176#102×C47C2314yes—
177#102×C47C2314yes—
178C4×C8×C47C2314yes—
179C24×C47—21no—
180C23×D47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—22no—
183C2×Q8×C47—22no—
184C2×Q8×C47C2412yes—
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47C2412yes—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2411yescharacteristic
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—24no—
199C22×Dic47—44no—
200C22×Dic47C2×D411yescharacteristic
201C22×Dic47C2×D411yescharacteristic
202C22×Dic47C2×D411yescharacteristic
203C22×Dic47C2×D411yescharacteristic
204C2×D188—21no—
205C2×D188—22no—
206C2×D188#4114yes—
207C2×D188C2412yes—
208C2×C4×D47—24no—
209C2×C4×D47—24no—
210C2×C4×D47—24no—
211C2×C4×D47—44no—
212C2×C4×D47—82no—
213C2×C4×D47—82no—
214C2×Dic94—24no—
215C2×Dic94—22no—
216C2×Dic94—22no—
217C2×Dic94—21no—
218C2×Dic94—24no—
219C2×Dic94—82no—
220C2×Dic94C2×D414yes—
221C2×Dic94C2412yes—
222C2×C8×C47—22no—
223C2×C8×C47—22no—
224C2×C8×C47C2412yes—
225C2×C8×C47C2412yes—
226C4⋊C4×C47—24no—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C22⋊C4×C47—24no—
233C22⋊C4×C47—24no—
234C42×C47C2×D412yes—
235C42×C47C2412yes—
236C22⋊Dic47—24no—
237C22⋊Dic47—24no—
238C22⋊Dic47—24no—
239#10625336—28no—
240#10625334—28no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243(C2×D47)⋊C4—24no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—24no—
247C4⋊Dic47—24no—
248C4⋊Dic47C2×D414yes—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4C2×D414yes—
257Dic47⋊C4C2×D414yes—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47C2×D412yes—
261C4×Dic47C2×D412yes—
262C4×Dic47C2412yes—
263C4×Dic47C2412yes—
264C2×C47⋊C8—22no—
265C2×C47⋊C8—22no—
266C2×C47⋊C8C2412yes—
267C2×C47⋊C8C2412yes—
268#10625325—28no—
269C23×C47—22no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47C22×D411yescharacteristic
274C22×D47—24no—
275C22×D47—22no—
276C22×D47—42no—
277C22×D47—42no—
278Q8×C47—22no—
279Q8×C47—22no—
280Q8×C47—42no—
281D4×C47—22no—
282D4×C47—22no—
283D4×C47—42no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47C22×D412yes—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C47C2×#4112yes—
296C2×C4×C472−1+412yes—
297C2×C4×C47C2511yescharacteristic
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—48no—
308C2×Dic47#13514yes—
309C2×Dic47C22×D412yes—
310C2×Dic47C22×D412yes—
311C2×Dic47C22×D412yes—
312C2×Dic47C22×D412yes—
313D188—24no—
314D188—22no—
315D188C2×#4114yes—
316C4×D47—48no—
317C4×D47—84no—
318C4×D47—84no—
319Dic94—28no—
320Dic94—22no—
321Dic94—22no—
322Dic94—42no—
323Dic94—84no—
324C8×C47—22no—
325C8×C47—22no—
326C47⋊C8—22no—
327C47⋊C8—22no—
328C2×#3360—471nomaximal, Sylow
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—84no—
333C22×C47#54812yes—
334C22×C47C2×#13512yes—
335C22×C47#57712yes—
336C22×C47C23×D411yescharacteristic
337C2×D47—24no—
338C2×D47—48no—
339C2×D47—42no—
340C2×D47—42no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47#54812yes—
347C4×C47C22×#4111yescharacteristic
348C4×C47C2×2−1+411yescharacteristic
349Dic47—22no—
350Dic47—22no—
351Dic47—22no—
352Dic47—42no—
353Dic47—42no—
354Dic47—42no—
355Dic47C2×#13514yes—
356C2×#556—471no—
357C2×#554—471no—
358#3360—4716no—
359C2×#488—471no—
360C2×#488D4711yescharacteristic, complemented
361C2×#487—471no—
362C2×#479—471no—
363C2×#479—471no—
364C2×#476—471no—
365C2×#463—471no—
366C2×#463—471no—
367C2×#461—471no—
368C2×C8×Q8—471no—
369C2×C4×SD16—471no—
370C2×C4×SD16—471no—
371C2×C4×D8—471no—
372C2×C47—82no—
373C2×C47#336014yescomplemented
374C2×C47C2×#54811yescharacteristic
375C2×C47C22×#13511yescharacteristic
376C2×C47C2×#57711yescharacteristic
377D47—44no—
378C22×SD16—471no—
379C22×SD16—471no—
380C22×D8—471no—
381#556—478no—
382#556—944no—
383#554—478no—
384#554—944no—
385C2×C4⋊Q8—471no—
386C2×C4⋊Q8—471no—
387C2×#126—941no—
388C2×#126—941no—
389C2×#125—471no—
390C2×#125C2×D4711yescharacteristic
391C2×#124—471no—
392C2×#124C2×D4711yescharacteristic
393C2×C22⋊Q8—941no—
394C2×C22⋊Q8—941no—
395C2×C22⋊Q8—941no—
396C2×C22⋊Q8—941no—
397C2×C4×Q8—471no—
398C2×C4×Q8—471no—
399C2×C4×Q8—471no—
400C2×C4×D4—471no—
401C2×C4×D4—471no—
402C2×C4×D4—471no—
403C2×C4×D4—471no—
404C2×#117—941no—
405C22×C4⋊C4—941no—
406#488—478no—
407#488C2×D4718yescomplemented
408#487—478no—
409#479—478no—
410#479—478no—
411#476—478no—
412#463—478no—
413#463—478no—
414#461—478no—
415C8×Q8—478no—
416C4×SD16—478no—
417C4×SD16—478no—
418C4×D8—478no—
419C2×#107—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×C4⋊C8—471no—
423C2×C4⋊C8—471no—
424C2×C4⋊C8—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103C2×D4711yescharacteristic
430C2×#103C2×D4711yescharacteristic
431C2×#102—471no—
432C2×#102—471no—
433C2×#102C2×D4711yescharacteristic
434C2×#102C2×D4711yescharacteristic
435C2×C4×C8—471no—
436C2×C4×C8—471no—
437C2×C4×C8C2×D4711yescharacteristic
438C47C2×#336011yescharacteristic, complemented, Sylow
439C22×Q8—471no—
440C22×Q8—471no—
441C22×Q8—941no—
442C22×Q8C22×D4711yescharacteristic
443C22×D4—471no—
444C22×D4C22×D4711yescharacteristic
445C23×C4—941no—
446C23×C4—941no—
447C23×C4—941no—
448C23×C4—941no—
449C2×SD16—474no—
450C2×SD16—474no—
451C2×SD16—944no—
452C2×SD16—944no—
453C2×D8—474no—
454C2×D8—944no—
455C22×C8—471no—
456C22×C8—471no—
457C22×C8C22×D4711yescharacteristic
458C22×C8C22×D4711yescharacteristic
459C4⋊Q8—474no—
460C4⋊Q8—474no—
461C4⋊Q8—942no—
462C4⋊Q8—942no—
463#126—948no—
464#126—948no—
465#125—22no—
466#125—474no—
467#125—942no—
468#125C22×D4714yes—
469#124—22no—
470#124—474no—
471#124—942no—
472#124C22×D4714yes—
473C22⋊Q8—948no—
474C22⋊Q8—948no—
475C22⋊Q8—948no—
476C22⋊Q8—948no—
477C4×Q8—474no—
478C4×Q8—474no—
479C4×Q8—474no—
480C4×Q8—474no—
481C4×Q8—942no—
482C4×Q8—942no—
483C4×D4—474no—
484C4×D4—474no—
485C4×D4—474no—
486C4×D4—474no—
487C4×D4—942no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4—942no—
491#117—948no—
492C2×C4⋊C4—21no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—948no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C22⋊C4—941no—
516C2×C22⋊C4—941no—
517C2×C42—471no—
518C2×C42—471no—
519C2×C42—941no—
520C2×C42—941no—
521C2×C42C22×D4711yescharacteristic
522#107—474no—
523#106—474no—
524#106—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527C4⋊C8—474no—
528#103—474no—
529#103—474no—
530#103—474no—
531#103—474no—
532#103C22×D4714yes—
533#103C22×D4714yes—
534#102—474no—
535#102—474no—
536#102C22×D4714yes—
537#102C22×D4714yes—
538C4×C8—474no—
539C4×C8—474no—
540C4×C8C22×D4714yes—
541C24—21no—
542C24—941no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—474no—
547C2×Q8—472no—
548C2×Q8—944no—
549C2×Q8—944no—
550C2×Q8—941no—
551C2×Q8—942no—
552C2×Q8—942no—
553C2×Q8—3762no—
554C2×Q8C23×D4712yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—474no—
559C2×D4—472no—
560C2×D4—941no—
561C2×D4—942no—
562C2×D4C23×D4712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—471no—
567C22×C4—471no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—944no—
571C22×C4—944no—
572C22×C4—944no—
573C22×C4—941no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—944no—
577C22×C4—3762no—
578C22×C4—3762no—
579C22×C4—1884no—
580C22×C4—1884no—
581C22×C4D4×D4711yescharacteristic
582C22×C4D4×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584SD16—948no—
585SD16—948no—
586D8—948no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—472no—
590C2×C8—472no—
591C2×C8—942no—
592C2×C8—942no—
593C2×C8C23×D4712yes—
594C2×C8C23×D4712yes—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—474no—
600C4⋊C4—474no—
601C4⋊C4—474no—
602C4⋊C4—472no—
603C4⋊C4—472no—
604C4⋊C4—944no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—941no—
612C4⋊C4—941no—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C42—472no—
624C42—472no—
625C42—472no—
626C42—472no—
627C42—944no—
628C42—944no—
629C42D4×D4712yes—
630C42C23×D4712yes—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—944no—
636C23—942no—
637C23—1882no—
638C23—1882no—
639C23C2×D4×D4711yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—42no—
643Q8—948no—
644Q8—942no—
645Q8—942no—
646Q8—3764no—
647Q8—1882no—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—474no—
652D4—944no—
653D4—942no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—474no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—472no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—3764no—
674C2×C4—3764no—
675C2×C4—1888no—
676C2×C4—1888no—
677C2×C4—1882no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4C2×D4×D4712yes—
681C2×C4C2×D4×D4712yes—
682C2×C4C2×D4×D4711yescharacteristic
683C2×C4#41×D4712yes—
684C2×C4#1309407112yes—
685C2×C4C24×D4711yescharacteristic
686C8—22no—
687C8—22no—
688C8—942no—
689C8—942no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—944no—
695C22—1888no—
696C22—1882no—
697C22—1882no—
698C22#1568978112yes—
699C22#135×D4712yes—
700C22#1568993012yes—
701C22C22×D4×D4711yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—474no—
708C4—942no—
709C4—942no—
710C4—942no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C4#1568978112yes—
715C4C2×#41×D4711yescharacteristic
716C4C2×#1309407111yescharacteristic
717C2—82no—
718C2—1884no—
719C2#2025603414yesdirect product factor
720C2C2×#1568978111yescharacteristic
721C2C2×#135×D4711yescharacteristic
722C2C2×#1568993011yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#488C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#488D47
hypocenterC47C2×#3360
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#15689842C2semidirect
2. C2×#15689829C2semidirect
3. #20256034C2direct (N × H)
4. C2×#15689476C2semidirect
5. C2×#15689472C2semidirect
6. C2×#15689428C2semidirect
7. C2×#15689427C2semidirect
8. C2×#15689411C2semidirect
11. C2×#15689327C2semidirect
12. C2×C8×Dic94C2semidirect
13. C2×C4×#10625325C2semidirect
14. C2×#15689208C2semidirect
16. C2×C47×#488C2semidirect
21. #15689842C22semidirect
23. #15689829C22semidirect
43. #15689476C22semidirect
44. #15689472C22semidirect
45. #15689428C22semidirect
46. #15689427C22semidirect
47. #15689411C22semidirect
50. #15689327C22semidirect
51. C8×Dic94C22semidirect
52. C4×#10625325C22semidirect
53. #15689208C22semidirect
71. C47×#488C22semidirect
360. C2×#488D47semidirect
373. C2×C47#3360semidirect
407. #488C2×D47semidirect
438. C47C2×#3360semidirect
719. C2#20256034direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#156898422
C2×#156898292
#202560342
C2×#156894762
C2×#156894722
C2×#156894282
C2×#156894272
C2×#156894112
C2×#156893372
C2×#156893352
C2×#156893272
C2×C8×Dic942
C2×C4×#106253252
C2×#156892082
C2×#156892032
C2×C47×#4882
C2×#336047